# Good software for solving a system of algebraic equations [closed]

I need to solve the following system of equations. solve([

a*c*e=a2*c2*e2, b*d*f=t*b2*d2*f2, t*a1*c1*e1=a3*c3*e3, b1*d1*f1=b3*d3*f3,

a*b*a1*b1=a2*b2*a3*b3, c*d*c1*d1=c2*d2*c3*d3, e*f*e1*f1=e2*f2*e3*f3,

b+c=b2+c2, d+e=d2+e2, b1+c1=b3+c3, d1+e1=d3+e3,

a1*b1*(b + c) + c*d*(b1 + c1) = a3*b3*(b + c) + c2*d2*(b1 + c1),

c1*d1*(d + e) + e*f*(d1 + e1) = c3*d3*(d + e) + e2*f2*(d1 + e1)

], [a2,b2,c2,d2,e2,f2,a3,b3,c3,d3,e3,f3], IgnoreSpecialCases,VectorFormat);

I tried to use some software to solve it. I can only solve it in the cases that most of a,b,c,d,e,f,a1,b1,c1,d1,e1,f1 are given by some numbers. Are there some good software which can solve this system of equations symbolically? Thank you very much.

## closed as off-topic by Andy Putman, Andrey Rekalo, abx, Suvrit, Will JagyMar 22 '14 at 18:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Andy Putman, Andrey Rekalo, abx, Suvrit, Will Jagy
If this question can be reworded to fit the rules in the help center, please edit the question.

• If you look at the "Related Questions" down the side of this page, you may find some where there have been answers you would find helpful. – Gerry Myerson Mar 22 '14 at 22:26

The Maple command $$sol := SolveTools:-PolynomialSystem({a*c*e = a2*c2*e2, b*d*f = t*b2*d2*f2, b1*d1*f1 = b3*d3*f3, a*b*a1*b1 = a2*b2*a3*b3, c*d*c1*d1 = c2*d2*c3*d3, e*f*e1*f1 = e2*f2*e3*f3, t*a1*c1*e1 = a3*c3*e3, b+c = b2+c2, b1+c1 = b3+c3, d+e = d2+e2, d1+e1 = d3+e3, a1*b1*(b+c)+c*d*(b1+c1) = a3*b3*(b+c)+c2*d2*(b1+c1), c1*d1*(d+e)+e*f*(d1+e1) = c3*d3*(d+e)+e2*f2*(d1+e1)}, {a2, a3, b2, b3, c2, c3, d2, d3, e2, e3, f2, f3}):$$ produces a long output which consists of $12$ elements. For example, the first one is $a2$ equals a rational function of the $13$ free variables $a, a1, a2, b, b1, c, c1, d, d1, e, e1, f, t$ of degree $17$. The others are similar. See the Maple output here https://www.dropbox.com/s/a8t6z5u2ukf0wt6/system.pdf as an exported PDF file. The PolynomialSystem command uses the Groebner basis tools.